This invention pertains to the field of interferometric profilometry or, more precisely, to the field of wave length-tuned phase-shifting interferometry. The invention is directed to a system and method capable of extracting multiple surface height information, simultaneously, from a set of phase-shifted, superimposed interferograms.
Phase shifting interferometry (PSI) is a highly accurate and efficient phase measuring method applied to a variety of applications including optical testing, surface profilometry, surface roughness estimation, and surface displacement measurement. The fundamental concept of PSI is that the phase of an interferogram can be extracted accurately by acquiring a set of phase-shifted interferograms. The phase shifts between interferograms are produced by changing the optical path difference (OPD) between the measurement surface and a reference surface. The phase shifts also can be achieved by changing the wave length, if the OPD between the measurement surface and the reference surface is not zero.
The United States patent to DeGroot U.S. Pat. No. 5,473,434 is directed to a phase shifting interferometer and method for achieving surface topography measurements. In the system of this patent, the phase shifts are produced by an assembly which mechanically physically displaces components of an interferometer to vary the length of the cavity. This patent is directed to an interferometric measurement of the surface topography of a single surface.
The United States patent to Sommargren U.S. Pat. No. 4,594,003 also is directed to an interferometer method and system to provide a phase map representing the optical path differences between a reference surface and an object surface. In the system disclosed in the '003 patent, the phase differences are produced by utilizing a diode laser light source, the wave length of which is varied; so that the phase difference between the two wave fronts producing the interference pattern is modulated by a known amount. The modulated interference pattern then is sensed with an imaging device; and the signals are processed to provide the desired phase map.
The systems of the U.S. Pat. Nos. 4,594,003 and 5,473,434 described above are representative of systems which are capable of providing phase measurements where there is only one surface involved. A number of applications exist, however, where the front and back surfaces of an object both impose interferograms on the recording plane simultaneously. In situations where this condition exists, most well known phase-shifting algorithms in PSI lose their ability to extract any individual phases from a set of phase-shifted superimposed interferograms.
To measure objects with multiple reflective surfaces, such as a transparent plate, the algorithms employed need to have the ability of extracting phases of any underlying interferogram from a set of intensity frames with superimposed interferograms. One such system for accomplishing this is described in the patent to DeGroot U.S. Pat. No. 5,488,477. This patent is directed to a PSI system for measuring the front and back surface topography of transparent objects which have substantially parallel surfaces. A relatively complex mathematical determination is employed in this patent to separate interference contributions due to the multiple reflections of the two parallel surfaces of the object. Among the procedures which are required by this patent are the reversing of the orientation of the object between two successive interference measurements. This then is followed by mathematical analysis or calculations to provide the desired profiles of the two different surfaces. A significant disadvantage of the system and method disclosed in this patent is the requirement of the reversing of the orientation of the object between measurements.
The United States patent to DeGroot U.S. Pat. No. 6,359,692 is directed to another method and system for profiling objects having multiple reflective surfaces. In the system and method of this patent, a phase-shifting algorithm using a Fourier transform, operating in conjunction with a Fizeau interferometer, is designed to extract the phases of a selected one of the multiple interference patterns produced by the different surfaces of the object. The algorithm is designed to select the patterns for only one of the surfaces. The algorithm then must be changed in order to select corresponding patterns for the other of the surfaces, while rejecting the patterns from the first surface. Different sets of measurements must be made for each of the surfaces employing a different algorithm to effect the desired filtering, so that comprehensive outputs can be obtained.
To measure objects with multiple reflective surfaces such as a transparent plate, any algorithm used must have the ability of extracting phases of an underlying interferogram from a set of intensity frames with superimposed interferograms. This is what is attempted by use of the Fourier transform algorithm of DeGroot '692. As mentioned above, however, this requires selecting a different Fourier transform algorithm for each of the surfaces of a multiple surface object. In general, a large number of intensity frames are needed, especially in case of measuring a thin translate plate (thickness<1 mm). If a measuring system cannot produce enough intensity frames, this algorithm may lose its ability to separate an interferogram of interest from a set of superimposed interferograms.
An algorithm which uses least-square fitting techniques to separate the front surface, back surface and thickness of a plate in PSI was reported by Ocada et al. in 1990 in a paper in Applied Optics, Vol.29, No.22, 1 Aug., 1990, pp. 3280 to 3285. The rms errors of the measurement for the surface shape are I/50 wavelengths in his paper. This measurement accuracy, however, is very difficult to achieve. One reason is that positioning of both the calibration object and the measurement object must be done with high precision. Even though there is a theoretical accuracy to this level, such a measurement accuracy has not been achieved in industrial applications. In addition, the high precision positioning requirements for accomplishing the types of results theoretically set forth in the Ocada paper preclude use of the Ocada system and method in a production line operation.
It is desirable to provide a method and system for measuring multiple reflective surfaces which overcomes the disadvantages of the prior art noted above, which is able to achieve sub-nanometer measurement accuracies, and which does not require high precision positioning requirements.